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Unit 8: Sources of Magnetic Field

Where a magnetic field comes from: a moving charge, a whole wire built from Biot-Savart pieces, and Ampere's shortcut for symmetric currents.

8 topics · 29 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

The Biot-Savart Law

  1. How it worksHow does the Biot-Savart law build a wire's total field by integrating over every small current element?
  2. Worked exampleFind the field 10 cm from a 2 mm current element carrying 5 amps, measured perpendicular to the wire.
  3. Ties togetherHow does the Biot-Savart law play the same role for magnetism that Coulomb's law plays for electric fields?
Your turn1 of 2
Find the magnetic field 36 cm from a 7 mm current element carrying 19 amps, measured perpendicular to the element. Use mu0/(4 π) = 1x10−7 T m/A.

The Field of a Long Straight Wire

  1. How it worksHow does integrating the Biot-Savart law over an infinite straight wire give a field that falls off as 1/r?
  2. Worked exampleFind the magnetic field 5 cm from a long straight wire carrying a current of 10 amps.
  3. Common mistakeWhy don't the magnetic field lines around a straight wire ever point toward or away from the wire itself?
  4. Going furtherWhat happens to the field around a straight wire as the distance from the wire keeps shrinking toward zero?
Your turn1 of 2
Find the magnetic field 35 cm from a long straight wire carrying a current of 33 amps. Use mu0 = 4 π times 10−7 T m/A.

The Force Between Two Parallel Currents

  1. How it worksHow does one wire's own magnetic field exert a force on the current flowing through a neighboring wire?
  2. Worked exampleFind the force per unit length between two wires 5 cm apart, each carrying 8 amps in the same direction.
  3. Going furtherWhat happens to the force between two parallel wires if the currents are made to run in opposite directions?
Your turn1 of 2
Find the force per unit length between two wires 35 cm apart, each carrying 20 amps in the same direction. Use mu0 = 4 π times 10−7 T m/A.

The Magnetic Field of a Current Loop

  1. How it worksHow does integrating the Biot-Savart law around a full loop give the field along the loop's own axis?
  2. Worked exampleFind the magnetic field at the center of a circular loop of radius 6 cm carrying a current of 4 amps.
  3. Going furtherWhat happens to a current loop's axial field as you move from its center out to a point far beyond it?
Your turn1 of 2
Find the magnetic field at the center of a circular loop of radius 15 cm carrying a current of 20 amps. Use mu0 = 4 π times 10−7 T m/A.

Ampere's Law

  1. How it worksHow does Ampere's law turn a magnetic field integral around a loop into a statement about enclosed current?
  2. Worked exampleFind the magnetic field 8 cm from a long straight wire carrying 15 amps, using an Amperian loop.
  3. How it worksWalk me through choosing an Amperian loop with enough symmetry to actually pull the field out of the integral.
  4. Ties togetherHow does Ampere's law act as the magnetic analogue of Gauss's law, built around a different geometry?
  5. Worked exampleFind the current enclosed by an Amperian loop where the magnetic field integrates to 2 times 10 to the -5 tesla-meters around it.
Your turn1 of 2
Find the magnetic field 35 cm from a long straight wire carrying 33 amps, using an Amperian loop. Use mu0 = 4 π times 10−7 T m/A.

Solenoids

  1. How it worksHow does Ampere's law applied to a rectangular loop through a solenoid give its interior field strength?
  2. Worked exampleFind the field inside a solenoid with 2000 turns per meter carrying a current of 3 amps.
  3. Common mistakeWhy is the magnetic field essentially zero everywhere just outside a long, tightly wound solenoid?
  4. Going furtherWhat happens to a solenoid's interior field if the number of turns per unit length is doubled?
  5. Common mistakeWhy doesn't a solenoid's interior field depend on the solenoid's own radius, only on its turns per length and current?
Your turn1 of 2
Find the field inside a solenoid with 2241 turns per meter carrying a current of 13 amps. Use mu0 = 4 π times 10−7 T m/A.

Toroids

  1. How it worksHow does Ampere's law applied to a circular path inside a toroid give a field that depends on the radius?
  2. Worked exampleFind the field inside a toroid of 500 turns carrying 2 amps, at a radius of 10 cm from its center.
  3. Ties togetherHow does a toroid's field formula reduce down to a solenoid's once the toroid's own radius grows very large?
Your turn1 of 2
Find the field inside a toroid of 727 turns carrying 13 amps, at a radius of 28 cm from its center. Use mu0 = 4 π times 10−7 T m/A.

Magnetism in Matter

  1. How it worksHow do aligned atomic magnetic domains in a ferromagnet add their own field on top of the solenoid's field?
  2. Common mistakeWhy isn't every material equally capable of being magnetized the way iron is?
  3. Going furtherWhat happens to a ferromagnet's alignment, and its magnetism, once it's heated above its Curie temperature?
Your turn1 of 2
Slipping an iron core inside a solenoid boosts its field by a factor of hundreds or thousands. If you replaced the iron core with aluminum instead, would you see a similarly dramatic boost?